Finite Time Bounded Control For A Class Of Nonlinear/Stochastic Systems

The continuous development of modern industry puts forward higher requirements for control system modeling and performance standards.Because of its important application in industrial process,nonlinear/stochastic system has become a research central issue in the field of control theory.On the other hand,finite time control is another research central issue in the field of control.In the analysis and synthesis of the control system,the stability analysis of the system is the basic problem to be considered first.Generally,the asymptotic stability in the infinite time domain reflects the steady-state performance of the system.However,in practical engineering systems,such as aerospace systems,robot control systems and other short-time control systems,in addition to their asymptotic stability,the transient performance of the control system should also be considered.In this thesis,the annular domain finite time bounded control problem for a class of nonlinear/stochastic system is discussed.The specific contents are as follows:(1)The problem of finite-time annular domain stabilization for nonlinear systems in strict-feedback form is considered.Firstly,for nonlinear systems,the definition of the stability in the finite-time annular domain is given.Secondly,by using the backstepping design method,the sufficient conditions for the existence of the finite time annular domain stability controller of nonlinear system are given,and the explicit expression of the controller is given.Finally,through two specific simulation examples,the correctness of the theoretical results is proved.Among them,Example 1 shows the correctness of the theoretical results;Example 2 compares and analyzes the advantage and disadvantages of the backstepping design method and the linear matrix inequality method.(2)The problem of annular finite-time stabilization control of stochastic linear time-varying systems with Wiener and Poisson perturbations is studied.By using the methods of linear matrix inequality and differential linear matrix inequality,the necessary and sufficient conditions for the system to be stable in the finite time annular domain are given.On this basis,a state feedback controller is designed.Furthermore,the numerical examples show the advantage of the method.(3)The problem of annular finite-time stabilization control for linear stochastic Markov jump systems driven by Wiener and Poisson noise is studied.Taking into account the factors of Markov jump,the model of the system becomes more complex,which makes the stability analysis and controller design of the system more difficult.Based on the characteristics of stochastic analysis method,matrix transformation technique,and Markov chain transition probability,the criterion for determining the stability of the stochastic system in finite time annular domain is given,and the state feedback controller is designed.Finally,a numerical examples is given to verify the correctness of the results.